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What is the length and width if perimeter 24 meters area 32 square meters?

Let's represent the length and width as \(l\) and \(w\) respectively.

From the given information we can write the following equation:

Perimeter: \(P = 2(l + w) = 24 meters\)

Area: \(A = l \times w = 32 square meters\)

From the perimeter equation, we can express \(l + w\) as:

$$l + w = \frac{24}{2} = 12 meters$$

Substituting the expression \(l + w = 12 meters\) into the area equation:

$$l \times w = 32 square meters$$

$$l \times (12 - l) = 32 square meters$$

$$12l - l^2 = 32 square meters$$

Rearranging the equation into the standard quadratic equation form:

$$l^2 - 12l + 32 = 0$$

Solving the quadratic equation for \(l\):

$$(l - 8)(l - 4) = 0$$

$$l_1 = 8 meters, l_2 = 4 meters$$

Since the length cannot be less than the width, we will consider \(l = 8 meters\) and \(w = 4 meters\).

Therefore, the length is \(8\) meters and the width is \(4\) meters.

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